{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "<p align=\"center\">\n",
    "    <img src=\"https://github.com/GeostatsGuy/GeostatsPy/blob/master/TCG_color_logo.png?raw=true\" width=\"220\" height=\"240\" />\n",
    "\n",
    "</p>\n",
    "\n",
    "## Data Science Basics in Python\n",
    "\n",
    "### Distribution Transformations\n",
    "\n",
    "#### Michael Pyrcz, Associate Professor, University of Texas at Austin \n",
    "\n",
    "##### [Twitter](https://twitter.com/geostatsguy) | [GitHub](https://github.com/GeostatsGuy) | [Website](http://michaelpyrcz.com) | [GoogleScholar](https://scholar.google.com/citations?user=QVZ20eQAAAAJ&hl=en&oi=ao) | [Book](https://www.amazon.com/Geostatistical-Reservoir-Modeling-Michael-Pyrcz/dp/0199731446) | [YouTube](https://www.youtube.com/channel/UCLqEr-xV-ceHdXXXrTId5ig)  | [LinkedIn](https://www.linkedin.com/in/michael-pyrcz-61a648a1)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Distribution Transformations in Python \n",
    "\n",
    "Here's a simple workflow, demonstration of bootstrap for modeling workflows. This should help you get started with this important data analytics method to evaluate and integrate uncertainty for any statistic or model.  \n",
    "\n",
    "#### Data Distribution Transformations\n",
    "\n",
    "Why do we perform distribution transformations?\n",
    "\n",
    "* variable has expected shape / correcting for too few data\n",
    "* a specific distribution assumption is required\n",
    "* correct for outliers\n",
    "\n",
    "How do we perform distribution transformations?:\n",
    "\n",
    "There are a variety of transformations. In general we are transforming the values from the cumulative distribution function (CDF), $F_{X}$, to a new CDF , $G_{Y}$. This can be generalized with the quantile - quantile transformation applied to all the sample data:   \n",
    "\n",
    "* The forward transform:\n",
    "\n",
    "\\begin{equation}\n",
    "Y = G_{Y}^{-1}(F_{X}(X))\n",
    "\\end{equation}\n",
    "\n",
    "* The reverse transform:\n",
    "\n",
    "\\begin{equation}\n",
    "X = F_{X}^{-1}(G_{Y}(Y))\n",
    "\\end{equation}\n",
    "\n",
    "This may be applied to any data, nonparametric or samples from a parametric distribution. We just need to be able to map from one distribution to another through percentiles, so it is a:\n",
    "\n",
    "* Rank preserving transform\n",
    "\n",
    "We will cover three examples including:\n",
    "\n",
    "1. Distribution rescaling\n",
    "2. Normal score transform\n",
    "\n",
    "#### Caveats\n",
    "\n",
    "I included methods that I have found useful for building my science and engineering workflows for subsurface modeling. \n",
    "\n",
    "* Accessibility for most scientists and engineers is my goal. \n",
    "* There are more advanced, more compact, more efficient methods to accomplish the same tasks. \n",
    "* I appreciate feedback and I will use it to improve these walk-throughs.\n",
    "\n",
    "#### Load and Configure the Required Libraries\n",
    "\n",
    "Let's start with my GeostatsPy package. It has a good Gaussian transformation algorithm."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import geostatspy.GSLIB as GSLIB          # GSLIB utilies, visualization and wrapper\n",
    "import geostatspy.geostats as geostats    # GSLIB methods convert to Python     "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now let's load standard packages for working with tabular and gridded data along with data visualization."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np                        # ndarrys for gridded data\n",
    "import pandas as pd                       # DataFrames for tabular data\n",
    "import os                                 # set working directory, run executables\n",
    "import matplotlib.pyplot as plt           # for plotting\n",
    "from scipy import stats                   # summary statistics"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Set the working directory\n",
    "\n",
    "I always like to do this so I don't lose files and to simplify subsequent read and writes (avoid including the full address each time). "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "#os.chdir(\"c:/PGE383/Examples\")             # set the working directory"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Loading Tabular Data\n",
    "\n",
    "Here's the command to load our comma delimited data file in to a Pandas' DataFrame object.  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Unnamed: 0</th>\n",
       "      <th>X</th>\n",
       "      <th>Y</th>\n",
       "      <th>Facies</th>\n",
       "      <th>Porosity</th>\n",
       "      <th>Perm</th>\n",
       "      <th>AI</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>0</td>\n",
       "      <td>100.0</td>\n",
       "      <td>900.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.101319</td>\n",
       "      <td>1.996868</td>\n",
       "      <td>5590.417154</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>1</td>\n",
       "      <td>100.0</td>\n",
       "      <td>800.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0.147676</td>\n",
       "      <td>10.711789</td>\n",
       "      <td>3470.845666</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>2</td>\n",
       "      <td>100.0</td>\n",
       "      <td>700.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0.145912</td>\n",
       "      <td>17.818143</td>\n",
       "      <td>3586.988513</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>3</td>\n",
       "      <td>100.0</td>\n",
       "      <td>600.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0.186167</td>\n",
       "      <td>217.109365</td>\n",
       "      <td>3732.114787</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>4</td>\n",
       "      <td>100.0</td>\n",
       "      <td>500.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0.146088</td>\n",
       "      <td>16.717367</td>\n",
       "      <td>2534.551236</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   Unnamed: 0      X      Y  Facies  Porosity        Perm           AI\n",
       "0           0  100.0  900.0     0.0  0.101319    1.996868  5590.417154\n",
       "1           1  100.0  800.0     1.0  0.147676   10.711789  3470.845666\n",
       "2           2  100.0  700.0     1.0  0.145912   17.818143  3586.988513\n",
       "3           3  100.0  600.0     1.0  0.186167  217.109365  3732.114787\n",
       "4           4  100.0  500.0     1.0  0.146088   16.717367  2534.551236"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df = pd.read_csv('https://raw.githubusercontent.com/GeostatsGuy/GeoDataSets/master/sample_data_MV_biased.csv') # load the datafile  \n",
    "df.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Gaussian Transformation 'by-Hand'\n",
    "\n",
    "Let's use basic code to perform a Gaussian transformation, step by step!\n",
    "\n",
    "1. for each data value calculate the cumulative percentile\n",
    "2. use the inverse of the Gaussian CDF to look up the value in Gaussian space for each percentile\n",
    "\n",
    "Here we transform the porosity feature to have the same distribution a parametric Gaussian distribution.\n",
    "\n",
    "To try out transformation to a nonparametric distribution change the commented out code to:\n",
    "\n",
    "```python\n",
    "#df['NPorosity'] = stats.norm.ppf(percentile,loc=mean,scale=stdev)           # inverse of Gaussian distribution\n",
    "df['NPorosity'] = np.percentile(df['Perm'].values,percentile*100)           # inverse of a non parametric distribution\n",
    "```\n",
    "and you will transform porosity to have the same distribution as permeability!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "mean = 0.0; stdev = 1.0\n",
    "\n",
    "percentile = df[\"Porosity\"].rank()/(len(df)+1)                              # unknown lower and upper tail\n",
    "# percentile = (df[\"Porosity\"].rank() - 1)/(len(df)-1)                      # known lower and upper tail\n",
    "# percentile = df[\"Porosity\"].rank()/len(df)                                # unknown lower tail\n",
    "# percentile = (df[\"Porosity\"].rank()-1)/len(df)                            # unknown upper tail\n",
    "\n",
    "df['NPorosity'] = stats.norm.ppf(percentile,loc=mean,scale=stdev)           # inverse of Gaussian distribution\n",
    "#df['NPorosity'] = np.percentile(df['Perm'].values,percentile*100)          # inverse of a non parametric distribution"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now let's visualize the original and transformed feature distributions."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 4 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.subplot(221)\n",
    "plt.hist(df['Porosity'],color='darkorange',edgecolor='black',alpha=1.0,bins=np.linspace(0.0,0.25,40))\n",
    "plt.xlabel('Porosity (fraction)'); plt.ylabel('Frequency'); plt.title('Original Feature Histogram')\n",
    "plt.xlim([0.025,0.22])\n",
    "\n",
    "plt.subplot(222)\n",
    "plt.hist(df['NPorosity'],color='darkorange',edgecolor='black',alpha=1.0,bins=np.linspace(-3,3,40))\n",
    "plt.xlabel('Gaussian Transformed Porosity'); plt.ylabel('Frequency'); plt.title('Transformed Feature Histogram')\n",
    "plt.xlim([-3.5,3.5])\n",
    "\n",
    "plt.subplot(223)\n",
    "plt.hist(df['Porosity'],color='red',edgecolor='black',alpha=1.0,bins=np.linspace(0.0,0.25,1000),cumulative=True,histtype='step')\n",
    "plt.xlabel('Porosity (fraction)'); plt.ylabel('Frequency'); plt.title('Original Feature CDF')\n",
    "plt.xlim([0.025,0.22])\n",
    "\n",
    "plt.subplot(224)\n",
    "plt.hist(df['NPorosity'],color='red',edgecolor='black',alpha=1.0,bins=np.linspace(-3.5,3.5,1000),cumulative=True,histtype='step')\n",
    "plt.xlabel('Gaussian Transformed Porosity'); plt.ylabel('Frequency'); plt.title('Transformed Feature CDF')\n",
    "plt.xlim([-3.5,3.5])\n",
    "\n",
    "plt.subplots_adjust(left=0.0, bottom=0.0, right=2.0, top=2.2, wspace=0.2, hspace=0.2); plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's calculate and look at the Q-Q plot.\n",
    "\n",
    "* since each value in original Porosity feature is linked to the values in the new transformed NPorosity feature, we can just scatter plot them.\n",
    "\n",
    "* note the units are very different so the position and slope are not helpful, but departure from a straight line inidcates a change in shape."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.subplot(111)\n",
    "plt.scatter(df['Porosity'].values,df['NPorosity'].values,color='darkorange',edgecolor='black')\n",
    "plt.xlabel('Original Feature - Porosity (fraction)'); plt.ylabel('Transformed Feature - NPorosity')\n",
    "\n",
    "plt.subplots_adjust(left=0.0, bottom=0.0, right=1.0, top=1.2, wspace=0.2, hspace=0.2); plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Gaussian Transformation with GeostatsPy\n",
    "\n",
    "The GeostatsPy package (Pyrcz et al., 2021) has a Gaussian transformation function based on the original Geostatistical Library (GSLIB, Deutsch and Journel, 1997)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "df['NPorosity_GeostatsPy'], tran_vr, tran_ns = geostats.nscore(df,'Porosity')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's visualize the transformed feature."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 4 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.subplot(221)\n",
    "plt.hist(df['Porosity'],color='darkorange',edgecolor='black',alpha=1.0,bins=np.linspace(0.0,0.25,40))\n",
    "plt.xlabel('Porosity (fraction)'); plt.ylabel('Frequency'); plt.title('Original Feature Histogram')\n",
    "plt.xlim([0.025,0.22])\n",
    "\n",
    "plt.subplot(222)\n",
    "plt.hist(df['NPorosity_GeostatsPy'],color='darkorange',edgecolor='black',alpha=1.0,bins=np.linspace(-3,3,40))\n",
    "plt.xlabel('Gaussian Transformed Porosity'); plt.ylabel('Frequency'); plt.title('Transformed Feature Histogram')\n",
    "plt.xlim([-3.5,3.5])\n",
    "\n",
    "plt.subplot(223)\n",
    "plt.hist(df['Porosity'],color='red',edgecolor='black',alpha=1.0,bins=np.linspace(0.0,0.25,1000),cumulative=True,histtype='step')\n",
    "plt.xlabel('Porosity (fraction)'); plt.ylabel('Frequency'); plt.title('Original Feature CDF')\n",
    "plt.xlim([0.025,0.22])\n",
    "\n",
    "plt.subplot(224)\n",
    "plt.hist(df['NPorosity_GeostatsPy'],color='red',edgecolor='black',alpha=1.0,bins=np.linspace(-3.5,3.5,1000),cumulative=True,histtype='step')\n",
    "plt.xlabel('Gaussian Transformed Porosity'); plt.ylabel('Frequency'); plt.title('Transformed Feature CDF')\n",
    "plt.xlim([-3.5,3.5])\n",
    "\n",
    "plt.subplots_adjust(left=0.0, bottom=0.0, right=2.0, top=2.2, wspace=0.2, hspace=0.2); plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Comments\n",
    "\n",
    "This was a basic demonstration of distribution transformations.\n",
    "\n",
    "I have other demonstrations on the basics of working with DataFrames, ndarrays, univariate statistics, plotting data, declustering, data transformations, trend modeling and many other workflows available at https://github.com/GeostatsGuy/PythonNumericalDemos and https://github.com/GeostatsGuy/GeostatsPy. \n",
    "  \n",
    "I hope this was helpful,\n",
    "\n",
    "*Michael*\n",
    "\n",
    "#### The Author:\n",
    "\n",
    "### Michael Pyrcz, Associate Professor, University of Texas at Austin \n",
    "*Novel Data Analytics, Geostatistics and Machine Learning Subsurface Solutions*\n",
    "\n",
    "With over 17 years of experience in subsurface consulting, research and development, Michael has returned to academia driven by his passion for teaching and enthusiasm for enhancing engineers' and geoscientists' impact in subsurface resource development. \n",
    "\n",
    "For more about Michael check out these links:\n",
    "\n",
    "#### [Twitter](https://twitter.com/geostatsguy) | [GitHub](https://github.com/GeostatsGuy) | [Website](http://michaelpyrcz.com) | [GoogleScholar](https://scholar.google.com/citations?user=QVZ20eQAAAAJ&hl=en&oi=ao) | [Book](https://www.amazon.com/Geostatistical-Reservoir-Modeling-Michael-Pyrcz/dp/0199731446) | [YouTube](https://www.youtube.com/channel/UCLqEr-xV-ceHdXXXrTId5ig)  | [LinkedIn](https://www.linkedin.com/in/michael-pyrcz-61a648a1)\n",
    "\n",
    "#### Want to Work Together?\n",
    "\n",
    "I hope this content is helpful to those that want to learn more about subsurface modeling, data analytics and machine learning. Students and working professionals are welcome to participate.\n",
    "\n",
    "* Want to invite me to visit your company for training, mentoring, project review, workflow design and / or consulting? I'd be happy to drop by and work with you! \n",
    "\n",
    "* Interested in partnering, supporting my graduate student research or my Subsurface Data Analytics and Machine Learning consortium (co-PIs including Profs. Foster, Torres-Verdin and van Oort)? My research combines data analytics, stochastic modeling and machine learning theory with practice to develop novel methods and workflows to add value. We are solving challenging subsurface problems!\n",
    "\n",
    "* I can be reached at mpyrcz@austin.utexas.edu.\n",
    "\n",
    "I'm always happy to discuss,\n",
    "\n",
    "*Michael*\n",
    "\n",
    "Michael Pyrcz, Ph.D., P.Eng. Associate Professor The Hildebrand Department of Petroleum and Geosystems Engineering, Bureau of Economic Geology, The Jackson School of Geosciences, The University of Texas at Austin\n",
    "\n",
    "#### More Resources Available at: [Twitter](https://twitter.com/geostatsguy) | [GitHub](https://github.com/GeostatsGuy) | [Website](http://michaelpyrcz.com) | [GoogleScholar](https://scholar.google.com/citations?user=QVZ20eQAAAAJ&hl=en&oi=ao) | [Book](https://www.amazon.com/Geostatistical-Reservoir-Modeling-Michael-Pyrcz/dp/0199731446) | [YouTube](https://www.youtube.com/channel/UCLqEr-xV-ceHdXXXrTId5ig)  | [LinkedIn](https://www.linkedin.com/in/michael-pyrcz-61a648a1)\n"
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